Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems We study the existence theory for parabolic variational inequalities in weighted L 2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L 2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs. Applied Mathematics and Optimization Springer Journals

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

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Copyright © 2008 by Springer Science+Business Media, LLC
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
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  • On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
    Albeverio, S.; Bogachev, V.; Röckner, M.

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